Dennis Delimarsky has authored a series of 17 articles on DZone that cover different aspects of the Flickr API structure. It covers the core parts of it that you most likely will want to integrate in your applications if you decide to use this web service.

Complete list of articles:

An Introduction
The Core – Signature
The Core – Getting the full token
Activity – User Photos
Activity – User Comments
Blogs
Collections
Contacts
Favorites
Groups – Base Methods
Group Membership
Group Pools
Uploading photos
People
Photos
UI – User Authentication
UI – Showing Profile Info